{
  "id": "2402.09851",
  "version": "v2",
  "published": "2024-02-15T10:15:06.000Z",
  "updated": "2024-09-04T06:20:49.000Z",
  "title": "A categorification for the characteristic polynomial of matroids",
  "authors": [
    "Takuya Saito",
    "So Yamagata"
  ],
  "comment": "25 pages, 2 figures",
  "categories": [
    "math.CO",
    "math.AT",
    "math.GT"
  ],
  "abstract": "In the present paper, we provide a cohomology group as a categorification of the characteristic polynomial of matroids. The construction depends on the ``quasi-representation'' of a matroid. For a certain choice of the quasi-representation, we show that our cohomology theory gives a generalization of the chromatic cohomology introduced by L. Helme-Guizon and Y. Rong, and also the characteristic cohomology introduced by Z. Dancso and A. Licata.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-09-04T06:20:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "05C15",
      "05C31",
      "57K18"
    ],
    "keywords": [
      "characteristic polynomial",
      "categorification",
      "cohomology group",
      "characteristic cohomology",
      "cohomology theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}